%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO013-4 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:14:45 AM UTC 2025
% Result : Unsatisfiable 0.49s 0.72s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 9 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
b != inverse(a),
file('theBenchmark.p',prove_a_inverse_is_b) ).
cnf(c1,axiom,
add(X,additive_identity) = X,
file('BOO004-0.ax',additive_id1) ).
cnf(c2,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO004-0.ax',multiplicative_id1) ).
cnf(c3,axiom,
add(a,b) = multiplicative_identity,
file('theBenchmark.p',b_a_multiplicative_identity) ).
cnf(c4,plain,
multiplicative_identity = add(a,b),
inference(equational,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(a,b) = additive_identity,
file('theBenchmark.p',b_an_additive_identity) ).
cnf(c6,plain,
additive_identity = multiply(a,b),
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
add(X,Y) = add(Y,X),
file('BOO004-0.ax',commutativity_of_add) ).
cnf(c8,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO004-0.ax',commutativity_of_multiply) ).
cnf(c9,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('BOO004-0.ax',additive_inverse1) ).
cnf(c10,plain,
add(X,inverse(X)) = add(b,a),
inference(equational,[status(thm)],[c4,c7,c9]) ).
cnf(c11,axiom,
multiply(X,inverse(X)) = additive_identity,
file('BOO004-0.ax',multiplicative_inverse1) ).
cnf(c12,plain,
multiply(X,inverse(X)) = multiply(b,a),
inference(equational,[status(thm)],[c6,c8,c11]) ).
cnf(c13,plain,
multiply(add(b,a),X) = X,
inference(equational,[status(thm)],[c2,c4,c7,c8]) ).
cnf(c14,plain,
multiply(X,add(b,a)) = X,
inference(equational,[status(thm)],[c2,c4,c7]) ).
cnf(c15,plain,
add(multiply(b,a),X) = X,
inference(equational,[status(thm)],[c1,c6,c7,c8]) ).
cnf(c16,plain,
add(X,multiply(b,a)) = X,
inference(equational,[status(thm)],[c1,c6,c8]) ).
cnf(c19,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO004-0.ax',distributivity2) ).
cnf(c30,plain,
add(multiply(X,b),multiply(X,a)) = X,
inference(equational,[status(thm)],[c14,c19]) ).
cnf(c35,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(add(Y,Z),X),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c42,plain,
add(multiply(X,b),multiply(a,X)) = X,
inference(equational,[status(thm)],[c8,c30]) ).
cnf(c43,plain,
multiply(b,inverse(a)) = inverse(a),
inference(equational,[status(thm)],[c8,c12,c16,c42]) ).
cnf(c75,plain,
add(multiply(X,Y),multiply(X,inverse(Y))) = X,
inference(equational,[status(thm)],[c10,c13,c35]) ).
cnf(c76,plain,
inverse(a) = b,
inference(equational,[status(thm)],[c15,c43,c75]) ).
cnf(g1,plain,
b = inverse(a),
inference(equational,[status(thm)],[c76]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO013-4 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 04:23:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.49/0.72 % SZS status Unsatisfiable
% 0.49/0.72 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------